Vegetarians and vegans can eat quite well in most countries. The traditional cuisine and the style of eating in many countries can make it a bit difficult for vegetarians or vegans to find food without animal products in it. However, most cultures have a at least a few vegetarian dishes, and many, if not most restaurants are willing to leave out or substitute animal ingredients.

Planning

Take your diet into consideration when planning your trip. Where will you be going? There will be a greater variety of food available in big urban centers then there will be in rural areas. If you want to visit a tiny village in rural Vietnam, fine, but be prepared that you may have to limit the variety in your diet, or work with restaurants or others feeding you to come up with food to your liking.

Research the cuisine for the place you are going. There will be a couple of vegetable/grain dishes everywhere so you'll have something to order in restaurants. This will also give you an idea of local cooking techniques; often times innocent looking vegetable dishes will be cooked in a meat stock, or contain fish sauce.

Look up lists of vegetarian restaurants and grocery stores in the area you'll be staying, check the destination guides for the area you will be visiting for information. Try local vegetarian groups in the area you'll be visiting.

Among countries in which vegetarianism and veganism is not the norm, those in the West tend to be the most accommodating, and even non-veg restaurants, particularly in the Netherlands, Denmark, the US and the UK, generally offer several vegetarian options.

Other countries, such as India and Taiwan, have a tradition of vegetarianism and so finding suitable meals in these places will not be a problem.

Explaining your diet

In many countries and cultures (especially developing countries where focus is often on getting any sort of food) vegetarianism/veganism is very rare or unheard of. People will feel insulted when you turn down the lamb kabobs they have prepared for you. Come up with a short explanation and be prepared to repeat it. If you're vegetarian/vegan for non-religious ethical reasons, in places with a language barrier or strong food/host tradition it's usually best to refrain from explaining out your beliefs and go with something inarguable (medical reasons, something vaguely religious or cultural). Be polite and apologetic as you would anywhere.

The tiny book Vegan Passport (ISBN 0907337309) contains a short explanation of what vegans eat, don't eat, and why. This is explained in about 40 languages, one page per language, and all you have to do is to show the right page to the restaurant staff. Another source of very brief listings of what vegans eat/don't eat, in many different languages, is available from the International Vegetarian Union's list of phrases.

In some cultures, there may be an internal vegetarian tradition of some kind that you can compare your diet to. In countries with Buddhist sub-populations, some vegetarian travellers find that calling their diet "Buddhist" is the simplest way to explain it.

Be as considerate as you are in your home country. If you are staying long term with someone or eating dinner at their house, let them know about your diet. Ask if you can bring food, give them examples of common local vegetarian dishes. Let them know that you don't mind them eating meat/milk/eggs/cheese.

When all else fails, hit the grocery store/local veggie market. You can cobble something together with a camping stove or get an apartment with a kitchen.